Research Area: geometry-topology

Research Profile: Geometry and Topology 
More specifically, I compute topological invariants, such as equivariant cohomology theories, of spaces with such structure. Symplectic geometry is the mathematical framework of classical physics; hyperkahler manifolds are symplectic manifolds wiht extra structure, are of particular recent interest due to their connections to theoretical physics. I am mainly concerned with the theory of symmetries of manifolds with these structures, as encoded by a Hamiltonian Lie group action, i.e. there exists a moment map on M encoding the action by Hamiltonian flows. Such group actions on symplectic and hyperkahler manifolds arise naturally in the context of physics, representation theory, and algebraic geometry. To a Hamiltonian space, one associates a symplectic (hyperkahler) quotient, which inherits a symplectic (hyperkahler) structure from the original manifold. The main theme of my recent research is the study of the topology and equivariant topology of these quotients, in particular the computation of their cohomology and complex K-theory rings.

Research Area: geometry-topology

Research Profile: Geometry and Topology 
More specifically, I compute topological invariants, such as equivariant cohomology theories, of spaces with such structure. Symplectic geometry is the mathematical framework of classical physics; hyperkahler manifolds are symplectic manifolds wiht extra structure, are of particular recent interest due to their connections to theoretical physics. I am mainly concerned with the theory of symmetries of manifolds with these structures, as encoded by a Hamiltonian Lie group action, i.e. there exists a moment map on M encoding the action by Hamiltonian flows. Such group actions on symplectic and hyperkahler manifolds arise naturally in the context of physics, representation theory, and algebraic geometry. To a Hamiltonian space, one associates a symplectic (hyperkahler) quotient, which inherits a symplectic (hyperkahler) structure from the original manifold. The main theme of my recent research is the study of the topology and equivariant topology of these quotients, in particular the computation of their cohomology and complex K-theory rings.

Research Area:  Algebra

Research Interests: My research area is commutative algebra and its connection to other areas like combinatorics and algebraic geometry. I am interested in homological invariants, edge ideals, simplicial complexes, sets of points in (multi)-projective spaces, toric ideals, symbolic powers of ideals, and combinatorial matrix theory

Research Area:  Algebra

Research Interests: My research area is commutative algebra and its connection to other areas like combinatorics and algebraic geometry. I am interested in homological invariants, edge ideals, simplicial complexes, sets of points in (multi)-projective spaces, toric ideals, symbolic powers of ideals, and combinatorial matrix theory